Convergence of spectral structures: a functional analytic theory and its applications to spectral geometry
Convergence of spectral structures: a functional analytic theory and its applications to spectral geometry
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DOI：
10.4310/cag.2003.v11.n4.a1
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发表时间：
2003
影响因子：
0.7
通讯作者：
K. Kuwae;T. Shioya
中科院分区：
文献类型：
--
作者：
K. Kuwae;T. Shioya
给出了Hilbert空间上一族谱结构上一些自然拓扑的泛函分析框架，并研究了由拉普拉斯引出的黎曼流形及其谱结构的收敛问题。我们还考虑了Alexandrov空间、局部有限图和具有Dirichlet形式的度量空间的收敛问题。我们的研究包括拉普拉斯具有连续谱的非紧(或不完备)空间的收敛。
We present a functional analytic framework of some natural topologies on a given family of spectral structures on Hilbert spaces, and study convergence of Riemannian manifolds and their spectral structure induced from the Laplacian. We also consider convergence of Alexandrov spaces, locally finite graphs, and metric spaces with Dirichlet forms. Our study covers convergence of noncompact (or incomplete) spaces whose Laplacian has continuous spectrum.